Time Dilation

I've noticed that when driving down a road, cars passing in the opposite direction appear to be going much faster than if viewed from a stationary position. I asked my friend how you could calculate how fast the other car appeared to be going and he said you just add your speed and the other car's speed.
I thought about this, and then had a question: if one object was going 75% the speed of light and an object going in the other direction was going 75% the speed of light as well, the apparent speed of the other object from the view of the first object would be 150% the speed of light. Since I know this is not possible, something has to change, but my friend is certain about his answer. What is the change?

On another thread in the recent past, I posted the result of adding 60 MPH and 60 MPH using the full relativistic formula. It's so close to 120 MPH that a regular calculator won't show the difference. Try it yourself using the formula posted in this thread. See how the "normal" way is close enough at human scale speeds, and why it's silly to make it more complicated in this regime?